Sigma-Aldrich Corp. (SIAL) went toe-to-toe against larger rival Thermo Fisher Scientific Inc. to acquire Life Technologies Corp. (LIFE), said people with knowledge of the matter, bidding through the weekend before falling short against Thermo’s $13.6 billion offer. St. Louis-based Sigma-Aldrich, which has a market capitalization of $8.9 billion, bid around $12.5 billion for Life, said the people, who asked not to be idenitified because the process was private. If successful, Sigma would have been one of the rare companies to acquire a bigger peer. Sigma-Aldrich, a producer of diagnostic and laboratory products, wanted to buy Carlsbad, California-based Life, which makes laboratory equipment that helps to map DNA, to gain market share and compete with Thermo Fisher. (TMO). “It was a scale play,” said Alex Morozov, an analyst with Chicago-based Morningstar Inc. (MORN), in a phone interview. “Sigma is a smaller player. If they want to compete with Thermo, they have to catch up in size.”